Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Constructing An Open Box

An open box with a square base is to be made from a square piece of cardboard 24 inches on a side by cutting out a square from each corner and turning up the sides.

Given:

Square = 24 inches on a side.

The little square that have been cut measures x inches by x inches and there are 4 little squares (one on each corner).

Express the volume V of the box as a function of the length x of the side of the square cut from each corner.

Let me see.

Volume of box = (edge)^3.

Area of each little square = x^2.

Length of each side of the square = 24 inches.

We want V(x).

My model is V(x) = (24 - x^2)^3.

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Constructing An Open Box

You haven't got the diagram right.  Start with a 24 by 24 square. Cut off the corner squares (x by x) so you have a sort of cross. When you fold up the four sides, the base of the box has dimensions (12-2x) by (12-2x) and height x.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Constructing An Open Box

You haven't got the diagram right.  Start with a 24 by 24 square. Cut off the corner squares (x by x) so you have a sort of cross. When you fold up the four sides, the base of the box has dimensions (12-2x) by (12-2x) and height x.

Bob

Ok. By the time I reached this problem, I was exhausted from the previous applications. Honestly, there is nothing more important in mathematics than the skill of forming models or equations or functions from the given data in word problems.